42 citations · 151 across the 15 of their papers we have counts for
5 papers · 1 filter
Conformally symplectic Chaplygin reduction in rubber rolling of surfaces of revolution over the plane
Jair Koiller
Rubber rolling (no-slip and no-twist) of a convex body on the plane under the influence of gravity is a SE(2) Chaplygin system, that reduces to the sphere of Poisson vectors. I com…
Vortices for lake equations (review with questions and speculations)
Jair Koiller
The `lake equation' on a planar domain D with bathymetry b(x,y) is given by $ \partial_t u + (u \cdot {\rm grad}) u= -{\rm grad}\, p \,, \,\,{\rm div} (b u) = 0 \,,\, \text{with}\,…
On the interplay between vortices and harmonic flows: Hodge decomposition of Euler's equations in 2d
Clodoaldo Grotta-Ragazzo, Björn Gustafsson, Jair Koiller
Let be a compact manifold without boundary whose first homology is nontrivial. Hodge decomposition of the incompressible Euler's equation in terms of 1-forms yields a coupled P…
Nonholonomic systems via moving frames: Cartan equivalence and Chaplygin Hamiltonization
Kurt Ehlers, Jair Koiller, Richard Montgomery +1
A nonholonomic system consists of a configuration space Q, a Lagrangian L, and an nonintegrable constraint distribution H, with dynamics governed by Lagrange-d'Alembert's principle…
Nonholonomic systems with symmetry allowing a conformally symplectic reduction
Pedro de M. Rios, Jair Koiller
Non-holonomic mechanical systems can be described by a degenerate almost-Poisson structure (dropping the Jacobi identity) in the constrained space. If enough symmetries transversal…